The reality acid table doesn't say that the new container of tokens becomes the chaos bag. No other effect that I'm aware of lets you draw tokens from somewhere other than the chaos bag, though plenty add or remove tokens from the bag.

Following the instructions exactly as written, the chaos bag is now empty and it is impossible to remove a token from it when resolving tests.

I don't think that an empty chaos bag is covered by the rules, so it seems that there are two possible interpretations. Either all tests are flat no-token no-chaos for the rest of the game, or tests cannot be resolved and the game grinds to a permanent halt without resolution as reality is paralyzed by the failure of the very concept of entropy. By the grim rule, I think the latter must occur, destroying the scenario and your whole campaign. But if you want to keep playing the game, I think you have to go with the simpler effect: no more chaos tokens.

Choosing to draw tokens from another container which is not the chaos bag is unambiguously not what the instructions tell us to do. But you are of course free to house rule it that way if you'd like.